Equivalent resistance between a and b -- Complex circuit

[kamhogo]

Homework Statement

Homework Equations

Req = [ ( 1 / R1) + ( 1 / R2) +. ...]^-1 (Parallel)
Req = R1 + R2 +. . . (Series )

The Attempt at a Solution

I tried to simplify the circuit by spreading it out but I guess something is wrong with my simplification since I can't arrive at the correct answer (7 ohms)...Can someone please point me in the right direction?h

 

[phyzguy]

You're taking the right approach, you just made a mistake. Look at the 10 Ohm resistor in the original drawing and in your first re-drawing. It is not just in series with the last 3 Ohm resistor, there is an extra connection that you left out of your re-drawing. Try doing the simplification again.

 

[kamhogo]

You're taking the right approach, you just made a mistake. Look at the 10 Ohm resistor in the original drawing and in your first re-drawing. It is not just in series with the last 3 Ohm resistor, there is an extra connection that you left out of your re-drawing. Try doing the simplification again.

Is this better? My answer is still a little off though...

 

[NascentOxygen]

In the original image you can see there is a piece of wire parallel to the 10 ohm resistor ...

 

[kamhogo]

In the original image you can see there is a piece of wire parallel to the 10 ohm resistor ...

Should I add a "dummy" 0 ohm resistor on that piece of wire...? Would it change anything?

 

[NascentOxygen]

The 0Ω is across the 10Ω, a parallel resistance of 0Ω.

 

[kamhogo]

The 0Ω is across the 10Ω, a parallel resistance of 0Ω.

But then I'd have to compute [(1/0)+(1/10) ]^-1...and 1/0 is undefined...or do I just leave it out of the calculation?

 

[NascentOxygen]

But then I'd have to compute [(1/0)+(1/10) ]^-1...and 1/0 is undefined...or do I just leave it out of the calculation?

I see.

It's 0/0 that is undefined; 1/0 is very large, infinity.

How about just thinking about it: what would a resistance meter measure if you had it connected to a 10Ω resistor and then you held a piece of thick wire across the resistor?

 

[kamhogo]

I see.

It's 0/0 that is undefined; 1/0 is very large, infinity.

How about just thinking about it: what would a resistance meter measure if you had it connected to a 10Ω resistor and then you held a piece of thick wire across the resistor?

It would read 10 ohms...

 

[NascentOxygen]

It would read 10 ohms...

It would read 0Ω, the wire is a short circuit.

If you had trouble using 0 in your computations, try instead a very small resistance, say 0.00001Ω and see where the calculations are heading...

 

[kamhogo]

It would read 0Ω, the wire is a short circuit

Please tell me more about short circuits. I haven't learned that yet...

 

[NascentOxygen]

Please tell me more about short circuits. I haven't learned that yet...

A short circuit is a piece of wire (a perfect conductor, ideally) that joins one node to another and causes all points along it to have the same voltage.

 

[kamhogo]

A short circuit is a piece of wire (a perfect conductor, ideally) that joins one node to another and causes all points along it to have the same voltage.

Ooooh. So the ideal 0 ohm wire would kind of force the 10 ohm resistor to be null? How does that work?

 

[cnh1995]

Ooooh. So the ideal 0 ohm wire would kind of force the 10 ohm resistor to be null? How does that work?

0 ohm in parallel with 10 ohm gives an equivalent resistance of 0 ohm between the two points.

 

[kamhogo]

It would read 0Ω, the wire is a short circuit.

If you had trouble using 0 in your computations, try instead a very small resistance, say 0.00001Ω and see where the calculations are heading...

I just tried the computation with 0.0001 ohm resistor in parallel with a 10 ohm resistor and I got 0. Wow! How can that be possible? Does it mean that the 10 ohms resistor might as well not be there?

 

[kamhogo]

I just tried the computation with 0.0001 ohm resistor in parallel with a 10 ohm resistor and I got 0. Wow! How can that be possible? Does it mean that the 10 ohms resistor might as well not be there?

Thanks everyone for your mentoring! Appreciated from the bottom of my heart!

 

[cnh1995]

Does it mean that the 10 ohms resistor might as well not be there?

Yes.

 

[NascentOxygen]

Ooooh. So the ideal 0 ohm wire would kind of force the 10 ohm resistor to be null? How does that work?

If you were an electron in a circuit and were given the choice, would you prefer to fight your way through a 10Ω resistance, or glide almost effortlessly along a copper conductor?

 

[epenguin]

I just tried the computation with 0.0001 ohm resistor in parallel with a 10 ohm resistor and I got 0. Wow! How can that be possible? Does it mean that the 10 ohms resistor might as well not be there?

Yes. In future you can just recognise it, and just forget any resistor in a position that is short-circuited like that, eliminate it and not include it in your calculation.

 

[kamhogo]

If you were an electron in a circuit and were given the choice, would you prefer to fight your way through a 10Ω resistance, or glide almost effortlessly along a copper conductor?

Second option! Thanks a lot for the image.